C2 chapter 2 - the sine and cosine rules

In this chapter we use the sine rule and cosine rule to 'solve' non-right triangles and also find the area of triangles using the area-sine formula.

Sections

C2 section 2.1

Before you start you should already be able to:

• use Pythagoras' theorem to solve problems involving the lengths of right-angled traingles
• use standard trigonometry with sin, cos and tan functions to find lengths and angles in right-angled triangles
• rearrange algebraic fractions including finding reciprocals

By the end of this section you will have learnt:

• the sine rule:

$\displaystyle \dfrac{a} {\sin{A}} = \dfrac{b} {\sin{B}} = \dfrac{c} {\sin{C}}$

• how to rearrange it using reciprocals to get:

$\displaystyle \dfrac{\sin{A}} {a} = \dfrac{\sin{B}} {b} = \dfrac{\sin{C}} {c}$

• how to substitute values into the first formula to solve problems involving certain missing sides in non-right triangles

Examples:

Proof:

C2 Exercise 2A

• C2 Exercise 2A worked solutions:

C2 Exercise 2A (the sine rule).jnt

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C2 Exercise 2A (the sine rule).pdf

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C2 section 2.2

Before you start you should already be able to:

• use the sine rule:

$\displaystyle \dfrac{a} {\sin{A}} = \dfrac{b} {\sin{B}} = \dfrac{c} {\sin{C}}$

• rearrange algebraic fractions by using reciprocals

By the end of this section you will have learnt:

• that taking reciprocals of each fraction we can easily derive:

$\displaystyle \dfrac{\sin{A}} {a} = \dfrac{\sin{B}} {b} = \dfrac{\sin{C}} {c}$

• how to substitute values into this new formula to solve problems involving certain missing angles in non-right triangles

C2 Exercise 2B

• C2 Exercise 2B worked solutions:

C2 Exercise 2C

• C2 Exercise 2C worked solutions:

C2 Exercise 2D

• C2 Exercise 2D worked solutions:

C2 Exercise 2E

• C2 Exercise 2E worked solutions:

C2 Exercise 2F

• C2 Exercise 2E worked solutions: